Can't add loop cut with Ctrl+R
That happens if you are using the Loop Cut on an edge that isn't connected to the rest of the mesh.


Try selecting that lower edge and moving it down a little. If it is not connected then just delete it. If the edge you select is connected but you see that there was another edge hiding below it then select that edge and move/delete it.

Or you could select everything and from the Tools panel on the left and use the Remove Doubles tool.